APPLICATION OF A STOCHASTIC REPRESENTATION IN NUMERICAL STUDIES OF THE RELAXATION FROM A METASTABLE STATE
De Pasquale Ferdinando 1, Mecozzi Antonio 2, Górecki Jerzy 3
1INFM and Department of Physics, University of Rome “La Sapienza”
Piazzale Aldo Moro 2, Roma, Italy
2INFMand Department of Electrical Engineering, University of L’Aquila
Poggio di Roio 67040, L ‘Aquila, Italy
3Institute of Physical Chemistry,
Polish Academy of Sciences and College of Science,
Kasprzaka 44/52, PL-01-224 Warsaw, Poland
1CM, Pawińskiego SA, PL-02-I06 Warsaw, Poland
DOI: 10.12921/cmst.2001.07.01.83-90
OAI: oai:lib.psnc.pl:517
Abstract:
We study the relaxation from a metastable state using a stochastic process which is related to the generating function of the system by means of Feynman-Kac formula. The results of such representation are compared with direct numerical simulations of the stochastic differential equations describing system’s evolution. We have found that the stochastic representation is more efficient from computational point of view then the direct simulations. The problems related to its numerical implementation are discussed.
References:
[1] N. G. van Kampen, Stochastic processes in physics and chemistry, North-Holland, Amsterdam 1987.
[2] C. W. Gardiner, Handbook of stochastic methods, Springer, Berlin 1987.
[3] M. Frankowicz, M. Malek-Mansour, F. Baras, Physica, A146, 650-656 (1987).
[4] M. Frankowicz, Acta Phys. Polon., A74, 444-460 (1988).
[5] P. E. Kloden, Numerical solution of stochastic differential equations, Springer, Berlin 1992.
[6] C. De Witt-Morette, K. D. Elworthy, A stepping stone to stochastic analysis in: C. De Witt-Morette and K. D. Elworthy (eds.) New stochastic methods in physics, Phys. Rep., 77, 125-168 (1981).
[7] A. Mecozzi, F. de Pasquale, L. Pelti, II Nuovo Cim., 100B, 733-745 (1987).
We study the relaxation from a metastable state using a stochastic process which is related to the generating function of the system by means of Feynman-Kac formula. The results of such representation are compared with direct numerical simulations of the stochastic differential equations describing system’s evolution. We have found that the stochastic representation is more efficient from computational point of view then the direct simulations. The problems related to its numerical implementation are discussed.
[1] N. G. van Kampen, Stochastic processes in physics and chemistry, North-Holland, Amsterdam 1987.
[2] C. W. Gardiner, Handbook of stochastic methods, Springer, Berlin 1987.
[3] M. Frankowicz, M. Malek-Mansour, F. Baras, Physica, A146, 650-656 (1987).
[4] M. Frankowicz, Acta Phys. Polon., A74, 444-460 (1988).
[5] P. E. Kloden, Numerical solution of stochastic differential equations, Springer, Berlin 1992.
[6] C. De Witt-Morette, K. D. Elworthy, A stepping stone to stochastic analysis in: C. De Witt-Morette and K. D. Elworthy (eds.) New stochastic methods in physics, Phys. Rep., 77, 125-168 (1981).
[7] A. Mecozzi, F. de Pasquale, L. Pelti, II Nuovo Cim., 100B, 733-745 (1987).
